Year: 2000
Paper: 1
Question Number: 10
Course: UFM Mechanics
Section: Momentum and Collisions 1
No solution available for this problem.
Difficulty Rating: 1516.0
Difficulty Comparisons: 1
Banger Rating: 1500.0
Banger Comparisons: 0
Three particles $P_1$, $P_2$ and $P_3$
of masses $m_{1}$, $m_{2}$ and $m_{3}$ respectively
lie at rest in a straight line on a smooth horizontal table.
$P_1$ is projected with speed $v$
towards $P_2$ and brought to rest by the collision.
After $P_2$ collides with $P_3$,
the latter moves forward with speed $v$. The coefficients of restitution
in the first and second collisions are $e$ and $e'$, respectively.
Show that
\[
e'=
\frac{m_{2}+m_{3}-m_{1}}{m_{1}}.
\]
Show that
$2m_1\ge m_2 +m_3\ge m_1$
for such collisions to be possible.
If $m_1$, $m_3$ and $v$ are fixed, find, in terms of $m_1$, $m_3$ and
$v$,
the largest and smallest possible
values for the final energy of the system.